Global existence for semilinear wave equations with scaling invariant damping in 3-D

Lai, N.; Zhou, Yi

doi:10.1016/j.na.2021.112392

Cited by 7 publications

(2 citation statements)

References 33 publications

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“…Under 1 < p p Str (n + µ) with µ ∈ (0, ∞), the lifespan estimates are improved in the papers [30,31,28] by applying an iteration argument associated with the modified Bessel functions. Concerning other studies on semilinear scaleinvariant damped wave equations, we refer to [22,19,17,23,15,25,21]. A recent important paper [18], related to the nonexistence of global solutions on Riemannian manifolds, is also recommended.…”

Section: Introductionmentioning

confidence: 99%

A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term

Chen

Fino

2023

DCDS-S

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<p style='text-indent:20px;'>In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula>, which can be represented by the Riemann-Liouville fractional integral of order <inline-formula><tex-math id="M2">\begin{document}$ 1-\gamma $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M3">\begin{document}$ \gamma\in(0, 1) $\end{document}</tex-math></inline-formula>. Our main interest is to study mixed influence from damping term and the memory kernel on blow-up conditions for the power of nonlinearity, by using test function method or generalized Kato's type lemma. We find a new competition, particularly for the small value of <inline-formula><tex-math id="M4">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula>, on the blow-up range between the effective case and the non-effective case.</p>

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Section: Introductionmentioning

confidence: 99%

A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term

Chen

Fino

2023

DCDS-S

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“…which has attracted more attention (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Wirth et al [13] obtained the energy solution to the Cauchy problem.…”

Section: Introductionmentioning

confidence: 99%

Lifespan Estimates of Solutions for a Coupled System of Wave Equations with Damping terms and Negative Mass terms∗

Yang

Ming

Han

et al. 2022

Discrete Dynamics in Nature and Society

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The main purpose of this paper is to study the formation of singularity for a coupled system of wave equations with damping terms, negative mass terms, and divergence form nonlinearities. Upper bound lifespan estimates of solutions to the system are obtained by using the iteration method. The results are the same as the corresponding coupled system of the wave equation with power nonlinearities v p and u q . To the best of our knowledge, the results in Theorems 1–5 are new. In addition, the variation trend of the wave is analyzed by using numerical simulation.

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Blow-up of solution to semilinear wave equations with strong damping and scattering damping

Ming

et al. 2022

Bound Value Probl

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This paper is devoted to investigating the initial boundary value problem for a semilinear wave equation with strong damping and scattering damping on an exterior domain. By introducing suitable multipliers and applying the test-function technique together with an iteration method, we derive the blow-up dynamics and an upper-bound lifespan estimate of the solution to the problem with power-type nonlinearity $|u|^{p}$ | u | p , derivative-type nonlinearity $|u_{t}|^{p}$ | u t | p , and combined type nonlinearities $|u_{t}|^{p}+|u|^{q}$ | u t | p + | u | q in the scattering case, respectively. The novelty of the present paper is that we establish the upper-bound lifespan estimate of the solution to the problem with strong damping and scattering damping, which are associated with the well-known Strauss exponent and Glassey exponent.

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Global existence for semilinear wave equations with scaling invariant damping in 3-D

Cited by 7 publications

References 33 publications

A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term

A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term

Lifespan Estimates of Solutions for a Coupled System of Wave Equations with Damping terms and Negative Mass terms∗

Blow-up of solution to semilinear wave equations with strong damping and scattering damping

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